I think Asuka just for some reason really wants to be close to tomoko, but tomoko's idol complex towards her kind of puts a barrier between them. Asuka's trying to relate on her stuff, picking schools together, studying together, its not working. Asuka's logic seems to be: "oh, you did (lewd thing) with your 'real friends?' Well do it with me too so we can be friends." But she's coming on too strong, and it just pushes Tomoko back.
This is definitely the right read of their relationship but I think that romantic interest os the only possible explanation for Asuka's actions that isn't contrived to some degree.